x2+y2-2(m+3)+2(1-4m2)y+16m4+9=0是一个圆,求半径r取值范围

[x-(m+3)]^2+[y+(1-4m^2)]^2=-16m^4-9+(m+3)^2+(1-4m^2)^2
所以r^2=-16m^4-9+(x+3)^2+(1-4m^2)^2>0

-16m^4-9+(m+3)^2+(1-4m^2)^2
=-16m^4-9+m^2+6m+9+16m^4-8m^2+1
=-7m^2+6m+1>0
7m^2-6m-1<0
-1/7<m<1

-7m^2+6m+1=-7(m-3/7)^2+16/7
-1/7<m<1
所以m=3/7,r^2=16/7
m=1,m=-1/7,r^2=0,但不取到
所以0<r^2<=16/7
0<r<=4√7/7

x2+y2-2(m+3)+2(1-4m2)y+16m4+9
=[(x-(m+3)]^2+[y+(1-4m^2)]^2+16m^4+9-(m+3)^2-(1-4m^2)^2=0
[(x-(m+3)]^2+[y+(1-4m^2)]^2
=(m+3)^2+(1-4m^2)^2-16m^4-9
=-7m^2+6m+1=r^2>0
当m=3/7时,r^2取最大值:16/7

半径r>0,
0<r<√(16/7),即为:
0<r<=4√7/7